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Full text of "Analytical Mechanics"

66.   Analysis of Motion.—The conception of motion necessarily involves four ideas, namely, the ideas of
(a)  A body which moves.
(b)  A second body with respect to which it moves.
(c)  A distance which it covers.
(d)  An interval of time during which the distance is covered.
67.   Relativity of Motion.    Reference System. — The first important inference to be drawn from the foregoing analysis is the fact that motion presupposes at least two bodies, namely, the body which is supposed to move and the body to which the motion is referred.    The words "motion'7 and "rest" become meaningless when applied to a single particle with no other body for reference.    Whenever we think or talk about the motion of a particle we refer its motion, consciously or unconsciously, to other bodies.    The body to which motion is referred is called a reference system. The choice of a particular body as a reference system is a question of convenience.    If a man walks in a crowded car fast enough to discommode its occupants he will be blamed, not because he is moving at the rate of, say, 20 miles per hour with respect to the ground, but because he is moving at the rate of 4 miles per hour with respect to the car.    In this case the car should be taken as the reference system, and not the ground.    On the other hand if the man wants, to leave the moving car, it is of great importance for him to*